The iconic striker, who is just one goal short of equalling the all-time goalscoring record, was offered a new contract after his previous deal expired at the end of the season.
But the 29-year-old has rejected the terms.
He told the club's official website: “I have absolutely loved my time at the club and would like to thank everyone for making my time there so special.
"The fans have been unbelievable and I can’t thank them enough for everything.
"The club has been a massive part of my life for the last six years and it’s sad to be leaving but now I am looking forward to the next stage of my career.”
Eastleigh, who last season won promotion into the Conference Premier, are managed by former U's player Richard Hill.
He was delighted to have secured Constable's services.
"I’ve spent the past two-and-a-half weeks speaking to James and telling him all about what we are striving to achieve here," Hill said.
"On the three occasions we’ve met, and during numerous telephone conversations, the subject of money has never been raised.
"In truth, James was keen to stay at Oxford and overhaul the club’s scoring record; a feat that after six years of committed service there he was desperate to achieve.
"He was initially holding out in the hope that Oxford would offer him fair terms to stay and do that.
"Oxford’s loss, though, is definitely our gain."
- You can leave your messages and tributes to Beano in the comments section below or email them to us and we shall pass them on to him.
Latest United news:
11:00am Monday 24th November 2014
OXFORD United were unable to break down a well-organised AFC Wimbledon side during their goalless draw at the Kassam Stadium on Saturday.
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9:30am Monday 24th November 2014
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8:40am Monday 24th November 2014
MICHAEL Appleton refused to be too downbeat and instead praised the way Oxford United stuck to the game plan as they drew a blank against AFC Wimbledon.
7:40am Monday 24th November 2014
ANDY Whing relished playing his part in restricting Adebayo Akinfenwa’s impact as Oxford United shared a goalless draw with AFC Wimbledon.